Scale Invariance and Beyond Les Houches Workshop, March 1014, 1997 [Paperback]

This book is an excellent introduction to the concept of scale invariance, which is a growing field of research with wide applications. It describes where and how symmetry under scale transformation (and its various forms of partial breakdown) can be used to analyze solutions of a problem without the need to explicitly solve it. The first part gives descriptions of tools and concepts; the second is devoted to recent attempts to go beyond the invariance or symmetry breaking, to discuss causes and consequences, and to extract useful information about the system. Examples are carefully worked out in fields as diverse as condensed matter physics, population dynamics, earthquake physics, turbulence, cosmology and finance.This book is an excellent introduction to the concept of scale invariance, which is a growing field of research with wide applications. It describes where and how symmetry under scale transformation (and its various forms of partial breakdown) can be used to analyze solutions of a problem without the need to explicitly solve it. The first part gives descriptions of tools and concepts; the second is devoted to recent attempts to go beyond the invariance or symmetry breaking, to discuss causes and consequences, and to extract useful information about the system. Examples are carefully worked out in fields as diverse as condensed matter physics, population dynamics, earthquake physics, turbulence, cosmology and finance.Lecture 1 Scale Invariance Without Mechanism?.- Lecture 2 Scale Invariance and Beyond: What Can We Learn from Wavelet Analysis?.- Lecture 3 Fractional Derivatives in Static and Dynamic Scaling.- Lecture 4 Multi-Dimensional Self-Similarity, and Self-Gravitating N-Body Systems.- Lecture 5 Scaling in Stock Market Data: Stable Laws and Beyond.- Lecture 6 Hysteresis, Avalanches, and Barkhausen Noise.- Lecture 7 Burgers Turbulence and the Energy Landscape of Randomly Pinned Objects.- Lecture 8 Power Laws and Scale Invariance in Physical Metallurgy.lóÇ